In Topic C, students know that the slope of a line describes the rate of change of a line. Students first encounter slope by interpreting the unit rate of a graph. In general, students learn that slope can be determined using any two distinct points on a line. Students verify this fact by checking the slope using several pairs of points and comparing their answers. In this topic, students derive y = mx and y = mx + b for linear equations by examining similar triangles.
Students generate graphs of linear equations in two variables first by completing a table of solutions, then using information about slope and y-intercept. Students graph equations using information about x- and y-intercepts. Next, students learn some basic facts about lines and equations, such as why two lines with the same slope and a common point are the same line, how to write equations of lines given slope and a point, and how to write an equation given two points.
Students compare two different proportional relationships represented by graphs, tables, equations, or descriptions. Finally, students learn that multiple forms of an equation can define the same line.
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